Army Overview
The Tyranids are known for their deadly close combat troops.
However, they do not have many long range or low AP weapons.
Thus most of their tactics involve getting close to the enemy.
This is not difficult as most Tyranids can be upgraded to leap or fly which can get them into combat on the second turn.

Tyranids are popular amongst hobbyists, as many of the models lend themselves to conversion because of all of their special biomorphs.

The Tyranids have a large number of special rules and upgrades.
The most important of these is known as Instinctual Behavior.
A Tyranid unit that is not within range of a synapse creature must take a leadership test.
If it fails it will fall back towards the nearest synapse creature of table edge.
Thus it is important for low leadership units like Termagants to be accompanied by a character with synapse.

Psycic Powers
The Tyranids have developed powerful psycic abilities.
One of these is Synapse.
In addition to avoiding Instinctual Behavior, Synapse prevents nearby units from being pinned, and keeps them fighitng to the last creature.
Most armies field several Synapse creatures.

Warp Field gives the creature a great armor save, as well as a rather poor invulnerable save.
I have not found this to be particularly useful, as monstrous creatures are usually targeted by weapons like Lascannons that ignore armor saves.

Warp Blast is one of the only low AP weapons in the Tyranid arsenal.
However, it has a reasonably short range, and is thus of limited utility.

The Shadow in the Warp can cripple enemy psykers by increasing their psycic test rolls.

Psycic Scream reduces the leadership of all enemy models within range.
This can be quite deadly now that you must pass a modified leadership test when you lose combat.

The Horror makes every enemy unit pass a leadership test to assault the creature.
It is commonly paired with Psycic Scream.

Catalyst functions similarly to Frag Grenades.

Biomorphs
Acid Maw allows the creature to reroll hits that fail to wound.
As most Tyranid creatures wound their prey so easily, this upgrade is not that useful.

Adrenal Glands can be used to increase the initiative or weapon skill of a unit.
The latter is almost always useful.
Increasing initiative is best used against Space Marines.

Bio Plasma provides an extra attack at a high initiative.
This can backfire by killing your opponent a thus preventing you from participating in the rest of the combat.

Enhanced Senses is essential for shooting.

Extended Carapace increases the armor of the character.
It is a great upgrade for Genesteelers.

Feeder Tendrils gives the model and any friendly unit within close range the preferred enemy special rule.

Flesh Hooks act like Frag Grenades.

Implant Attack doubles the number of unsaved wounds that the model inflicts.

Lash Whip decreases the number of close combat attacks of opponents in close combat.

Leaping gives the unit a 12" assault move.

Rending Claws give the model the Rending special rule.

Scuttlers give the model an extra 6" move.
This is obviously more useful than Leaping, but both are good upgrades.

Scything Talons give the model an extra attack.

Symbiote Rippers are just plain bad.

Toxic Miasma functions like Adrenal Glands.

Toxin Sacs halves the number of wounds but insta kills toughness 3 or lower creatures.

Winged allows the character to move like a Jump Troop.

Monstrous Creature Biomorphs

Bonded Exoskeleton increases the toughness of the creature.
It is a great upgrade as attacks from weak creatures such as Howling Banshees can no longer harm the creature.

Crushing Claws given you a random number of attacks.
It is not worth taking, as the expected number of attacks is not much greater than your regular number, and you can roll poorly and have many fewer attacks than expected.

Regeneration is a powerful upgrade that lets you ignore wounds.
However it is too expensive.

Reinforced Chitin increases the number of wounds of the creature.
It is worth the points.

Spine Bank

Spore Cyst is just terrible.
It can even hurt the creature you give it to.

Symbiote Rippers work in combintation with Thornback.

Tail Mace gives you an extra attack if the creature is in combat with at least four models.
It is worth the points.

Tail Scythe is more deadly than the Mace, but is more expensive.

Thornback gives a negative modifier to the enemy's leadership check if you win combat.
This can really help break units and win games.

Tusks give you an extra attack when charging.
They are not as good as Scything Talons.

Weapons Arsenal
The Barbed Strangler has a long range and uses the large blast template.
It is useful for killing Imperial or Tau gunlines.
As an added bonus it also causes pinning.
Its one downside, and that of most Tyranid weapons, is that it has a high AP value.

The Deathspitter is a slightly shorter range version of the Barbed Strangler.
It uses a smaller template but has a higher strength.

The Devourer is a medium ranged assault weapon.
It can fire multiple times but does not have a template.

The Fleshborer is a close ranged assault weapon.

The Spinefist is similar to the Fleshborer, but has a lower strength.
However, it is more accurate thanks to the fact that it is twin linked.

The Venom Cannon is the Tyranids other long range weapon.
It has a slightly better AP value than the Barbed Strangler, and also has higher strength.
The downside is that it does not use a blast template.

HQ
Hive Tyrants
Hive Tyrants have Synapse.
They can also be given wings.
This makes them ideal characters to keep Hormagaunts in line, as the little critters run so fast that other characters can't keep them within Synapse range.
Toxic Miasma and Flesh Hooks make the Tyrant a real beast in hand to hand combat.

Tyrant Guard
As their name implies, these creatures protect the Hive Tyrant.
Popular upgrades include Flesh Hooks, Implant Attack, and Lash Whip.

Broodlord
These are incredibly deadly characters.
They have a tendency to surprise novice opponents, as they do not look nearly as threatening as Warriors or Carnifexes.
They are usually given Extended Carapace, Flesh Hooks and Toxin Sacs.
Make sure that he is never without a retinue of at least 6 Genesteelers.

Elite
Lictor
There is much debate as to the utility of Lictors.
I have found them to be very useful.
You can use them to tie up heavy weapons teams, or immobilize tanks.
This can give your other troops the time they need to close with the enemy.
Alternatively they can be used like light cavalry, with hit and run type tactics.
Their ability to blend into the surrounding terrain helps minimize damage from shooting.
They also help other troops come in from reserve.

Tyranid Warriors
These can be outfitted to be deadly in hand to hand combat, or as long range fire support.
Popular hand to hand upgrades include Scything Talons, Rending, and Leaping.
Enhanced Senses, Toxin Sacs, and Venom Cannons make a good long range gun platform.
Extended Carapace is beneficial in hand to hand combat and at long range.
Like the Hive Tyrant, Tyranid Warriors have Synapse and can also be given Wings.

Troops
Genesteeler
These are some of the most deadly close combat troops in the game.
Most armies include at least one squad.
They are given Extended Carapace to boost their armor save, and Scuttle to get them into combat sooner.

Termagants
These guys are not the best troops, but they sure are cheap.
They seem to work well in squads of 10 to 20.
Without Number can be very useful.

Hormagaunts
These are the hand to hand version of Termagants.
Take them in large numbers, i.e. 15 to 25.
Leaping helps them get into combat faster.

Ripper Swarm
Point for point Ripper Swarms are a great value.
In practice, they do not replace Hormagaunts.

Fast Attack
Ravener
These are expensive, but worth the points.
They are generally given Scything Talons and Rending.

Gargoyle
Gargoyles are basically Termagants with wings and guns.
Like the Raveners, Gargoyles are expensive.
They are incrediably useful.

Red Terror

Heavy
Carnifex
These can be outfitted as heavy support or as hand to hand monsters.
The Venom Cannon is the weapon of choice for long range shooting.
The new rules for running have made the hand to hand option more viable than before.

Zoanthrope
These are the primary Synapse creatures in a Tyranid army.
So if you are planning on taking lots of Gaunts then make sure that you bring along some of these.

Biovore
These are as close to artillery as you find in standard Tyranid armies.